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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
8.5 | $C_2^3$ | $2^{3}$ | $2$ | $8$ | $C_2^3$ | Abelian - 3 |
12.3 | $A_4$ | $2^{2} \cdot 3$ | $2 \cdot 3$ | $4$ | $C_1$ | Solvable - 2 |
16.3 | $C_2^2:C_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.10 | $C_2^2\times C_4$ | $2^{4}$ | $2^{2}$ | $16$ | $C_2^2\times C_4$ | Abelian - 3 |
16.11 | $C_2\times D_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.12 | $C_2\times Q_8$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.13 | $D_4:C_2$ | $2^{4}$ | $2^{2}$ | $10$ | $C_4$ | Nilpotent - 2 |
16.14 | $C_2^4$ | $2^{4}$ | $2$ | $16$ | $C_2^4$ | Abelian - 4 |
18.4 | $C_3:S_3$ | $2 \cdot 3^{2}$ | $2 \cdot 3$ | $6$ | $C_1$ | Solvable - 2 |
24.8 | $C_3:D_4$ | $2^{3} \cdot 3$ | $2^{2} \cdot 3$ | $9$ | $C_2$ | Solvable - 2 |
24.13 | $C_2\times A_4$ | $2^{3} \cdot 3$ | $2 \cdot 3$ | $8$ | $C_2$ | Solvable - 2 |
24.14 | $C_2\times D_6$ | $2^{3} \cdot 3$ | $2 \cdot 3$ | $12$ | $C_2^2$ | Solvable - 2 |
24.15 | $C_2^2\times C_6$ | $2^{3} \cdot 3$ | $2 \cdot 3$ | $24$ | $C_2^2\times C_6$ | Abelian - 3 |
27.3 | $\He_3$ | $3^{3}$ | $3$ | $11$ | $C_3$ | Nilpotent - 2 |
27.5 | $C_3^3$ | $3^{3}$ | $3$ | $27$ | $C_3^3$ | Abelian - 3 |
32.2 | $C_2.C_4^2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.5 | $C_2^2:C_8$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.6 | $C_2^3:C_4$ | $2^{5}$ | $2^{2}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.7 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.8 | $C_4.D_4$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.9 | $D_4:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.10 | $Q_8:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.11 | $C_4\wr C_2$ | $2^{5}$ | $2^{3}$ | $14$ | $C_4$ | Nilpotent - 3 |
32.21 | $C_2\times C_4^2$ | $2^{5}$ | $2^{2}$ | $32$ | $C_2\times C_4^2$ | Abelian - 3 |
32.22 | $C_2^3:C_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.23 | $C_2^2.D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.24 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.25 | $C_4\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.26 | $C_4\times Q_8$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.27 | $C_2^2\wr C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.28 | $C_4:D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.29 | $C_2^2:Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.30 | $C_2^2.D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.31 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.32 | $C_4.Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.33 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.34 | $C_4:D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.35 | $C_4:Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.36 | $C_2^2\times C_8$ | $2^{5}$ | $2^{3}$ | $32$ | $C_2^2\times C_8$ | Abelian - 3 |
32.37 | $C_2\times \OD_{16}$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.38 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $20$ | $C_8$ | Nilpotent - 2 |
32.39 | $C_2\times D_8$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.40 | $C_2\times \SD_{16}$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.41 | $C_2\times Q_{16}$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.42 | $D_8:C_2$ | $2^{5}$ | $2^{3}$ | $14$ | $C_4$ | Nilpotent - 3 |
32.43 | $D_8:C_2$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.44 | $Q_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.45 | $C_2^3\times C_4$ | $2^{5}$ | $2^{2}$ | $32$ | $C_2^3\times C_4$ | Abelian - 4 |
32.46 | $C_2^2\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.47 | $C_2^2\times Q_8$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |